1. Field of the Invention
The invention relates to multi-channel communication systems.
2. Discussion of the Related Art
This section introduces aspects that may be helpful to facilitating a better understanding of the inventions. Accordingly, the statements of this section are to be read in this light and are not to be understood as admissions about what is in the prior art or what is not in the prior art.
A variety of communication systems use multiple channels to increase data rates and/or to separate different data streams being communicated. In such systems, the different channels share part of a physical communications medium, which causes inter-channel crosstalk. Such inter-channel crosstalk typically means that the communications transmitted to one channel are, to some extent, received on one or more other channels. The inter-channel crosstalk or interference is typically undesirable.
Many multi-channel communication systems can be described by the linear crosstalk models. The linear crosstalk model defines relations between transmitted and received signals in a single communication time slot as follows:Y=H·X+V  (1)In eq. (1), the N-component complex vectors X, Y, and V represent the transmitted signal, the received signal, and the noise signal, respectively. The j-th components Xj, Yj, and Vj of these vectors are the values of the transmitted signal, the received signal, and the noise signal on the J-th channel. Herein, the N×N complex matrix, H, will be referred to as the channel matrix. The (j, m)-th component Hj,m describes how the physical communication channel produces a signal on the j-th channel in response to a signal being transmitted to the m-th channel. In particular, diagonal elements of the channel matrix, H, describe direct channel couplings, and off-diagonal elements of the channel matrix, H, describe inter-channel crosstalk.